Elementary mathematics
Positive numbers Addition 5+0\quad=\quad0+5\quad=\quad5 \\ 5+1\quad=\quad1+5\quad=\quad6 \\ 5+2\quad=\quad2+5\quad=\quad7 \\ 5+3\quad=\quad3+5\quad=\quad8 \\ 5+4\quad=\quad4+5\quad=\quad9 \\ 5+5\quad=\quad5+5\quad=\quad10 ¹ 27 + 59 ———— 86 Multiplication 5 \cdot 0 \quad = \quad 0 \cdot 5 \quad = \quad 0 \\ 5 \cdot 1 \quad = \quad 1 \cdot 5 \quad = \quad 5 \\ 5 \cdot 2 \quad = \quad 2 \cdot 5 \quad = \quad 5 + 5 \\ 5 \cdot 3 \quad = \quad 3 \cdot 5 \quad = \quad 5 + 5 + 5 \\ 5 \cdot 4 \quad = \quad 4 \cdot 5 \quad = \quad 5 + 5 + 5 + 5 | | |} 2 4 × 3 7 ------ 1 6 8 + 7 2 ---------- = 8 8 8 Powers 5^0 = 1 \\ 5^1 = 5 \\ 5^2 = 5 \cdot 5 \\ 5^3 = 5 \cdot 5 \cdot 5 As you can see in the following table, raising numbers to powers results in very large numbers. You will not need to memorize this table. It will occasionally be useful to know the squares of numbers but you can easily work that out in your head by multiplying the number times itself. From Wikipedia:Exponentiation: Negative numbers Subtraction is the opposite of addition. : 5-3=2\quad because \quad2+3=5 But then what is : 3-5=? What number when added to 5 results in 3? The answer is that there is no answer. So we have to create one. We therefore create what are called negative numbers From Wikipedia:Negative number Negative numbers are usually written with a minus sign in front. Negative numbers can be thought of as resulting from the subtraction of a larger number from a smaller. For example, negative three is the result of subtracting three from zero: :   −3.}} Addition Adding a negative number is the same as subtracting a positive number. :   2}}. Addition of two negative numbers is very similar to addition of two positive numbers. For example, :   −8}}. Subtraction Subtracting a negative number is the same as adding a positive number. :   5 + 3     8}} and :   (−5) + 8     3}}. Multiplication When multiplying numbers, the magnitude of the product is always just the product of the two magnitudes. The sign of the product is determined by the following rules: * The product of two positive numbers is positive. * The product of one positive number and one negative number is negative. * The product of two negative numbers is positive. Thus :   6}} and :   −6}} and :   6}}. Fractions Division Division is the opposite of multiplication. :: \frac{6}{3} = 2 \quad because \quad 2 \cdot 3 = 6 The sign rules for division are the same as for multiplication. For example, :: \frac{\phantom{-}8}{-2}=-4 :and :: \frac{-8}{\phantom{-}2}=-4 :and :: \frac{-8}{-2}=4 If dividend and divisor have the same sign, the result is always positive. Another method of dividing negative numbers is that if one of the numbers being divided is a negative, the answer will be negative. Further reading *Introductory mathematics References